Data Presentation
Figure 6. Scatter plot showing walleye (Sander vitreus) mean total length (mm) as a function of mean annual temperature (°C).
Figure 7. a) Box plot showing total catch per unit effort (fish day-1) of walleye (Sander vitreus) for depth categories (m) and b) boxplots of catch per unit effort (fish day-1) for categories of angling pressure. Boxplots are paired with half-violin plots to help visualize the distribution of the data.
Results
Preliminary graphical explorations of raw data revealed a quadratic relationship between TL and MAT (Fig 6). However, only the lower values of this curve were visible. This is because walleye are constrained by low temperatures at high latitudes. In future climate scenarios, the descending limb of this quadratic relationship may be visible as walleye length becomes constrained by warm temperatures at lower latitudes. CPUE was significantly skewed away from the mean for both depth and angling pressure (Fig 7). For depth, the medians are highly skewed to the upper and lower limits of data coverage (Fig 7). For angling pressure, the median is ~38 fish per day (Fig 7).
Statistical Analysis
Non-linear modelling
To determine the effect of MAT (°C) on TL (mm) we created three models: 1) parabolic (non-linear), 2) linear, and 3) exponential (non-linear). We fitted these models to our observed data using the nls function in R (R Core Team 2017) and providing estimated start values for each function (Fig 8). To avoid overfitting our models, we used AIC (Burnham and Anderson 2002) to select the most supported model. According to Burnham and Anderson (2002), the model with the lowest AIC value is the most parsimonious, or the ‘best’. In other words, AIC balances model fit with complexity. Models with ΔAIC < 2.00 were considered equally supported (Burnham and Anderson 2002).
Figure 8. Scatter plot of walleye (Sander vitreus) total length (mm) as a function of mean annual temperature (°C) for 100 lakes in Canada with parabolic, exponential, and linear functions predicting the relationship.
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Table 2. AIC table comparing models predicting the relationship between total length (mm) of walleye (Sander vitreus) and mean annual temperature (°C). Models include parabolic, exponential, and linear, with equations presented for each. Additionally, we report AIC, change in AIC (ΔAIC), and AIC weight for each model.
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The parabolic equation was the most supported model (ΔAIC = 0), and accounted for 99% of AIC weight (Table 2; Fig. 8). We used the most supported model to predict total walleye length for all lakes in our study area under a 8.5 ˚C warming scenario (Fig 10). The second most supported model (ΔAIC = 8.82) was the exponential model (Table. 2; Fig. 8). The exponential model had a ΔAIC > 2.00 and therefore was not equally supported. The linear model was the least supported model (ΔAIC = 67.98; Table 2; Fig. 8).
ANCOVA
We modelled the effect of depth and angling pressure on CPUE using ANCOVA. Depth and angling pressure were each independent class variables, CPUE was the continuous response variable and lake area was a covariate. To test for an interaction between depth and angling pressure, we constructed the model as follows:
anova(lm(CPUE ~ DEPTH*APRESS + AREA)
The interaction between lake depth and angling pressure explained the highest proportion of variance in our ANCOVA model (Sum Sq = 92234; Proportion of variance explained = 0.98), and effectively cancelled out the individual effect of depth and angling pressure (Table 3). The interaction term had an F-value of 11363, indicating a positive and large signal to noise ratio (Table 3). This F-value, combined with the large proportion of variance explained and the low p-value, enable us to be confident in stating that the interactive effect of depth and angling pressure on CPUE is indeed significant and meaningful (Table 3). The results for the individual effects of lake depth and angling pressure are irrelevant given the strong effect of the interaction term. In comparison, despite having a P-value < 0.05, the lake area accounted for only 1% of the variance and had a much smaller F-value (signal to noise ratio) of 145 (Table 3). The proportion of variance explained by residuals (error) was less than 1%, providing further evidence that our model adequately explains observed variation in CPUE (Table 3).
Table 3. Output from ANCOVA test conducted in R Studio (R Core Team 2017) modelling the effect of depth, angling pressure, and lake area on catch per unit effort of walleye (Sander vitreus).
Discussion
ANCOVA
We created an interaction plot to visualize the relationship (Fig 9). The interaction plot reveals that CPUE decreases in shallow lakes with high angling pressure and deep lakes with low angling pressure, suggesting that lakes are overfished in the former and devoid of fish in the latter. To contrast, CPUE increases in shallow lakes with low angling pressure, and deep lakes with high angling pressure. This suggests that deep lakes provide refugia from angling pressure, and that the interaction between lake depth and angling pressure better explains walleye abundance lake depth or angling pressure on their own.
Figure 9. Interaction plot showing the interactive effect of angling pressure and lake depth on catch per unit effort for walleye (Sander vitreus).
Non-linear regression
We used the parabolic model to predict changes in walleye length for all 100 lakes in our study area. Figure 10 shows the expected change in walleye length for three lakes in our study area under a 8.5 RCP warming scenario in the year 2085. Lake Simcoe Ontario had the highest historical MAT in our study area, at 9.9˚C. The mean total length of walleye in this lake was 483 mm. After applying the climate change projection, MAT increased to 14.3 ˚C, while total length decreased by 128 mm to 355 mm. Jackson Lake Alberta had the median value for historical mean annual temperature (2.4 ˚C), and a mean walleye length of 420 mm. After applying the climate change prediction model, MAT increased to 7.6 ˚C, and mean walleye length increased by 47 mm to 467 mm. Finally, Lake Tice Manitoba had the lowest historical MAT in our study area at -7.7 ˚C. The mean total length of walleye in this lake was only 129 mm. After applying the climate prediction model, MAT increased to -2.1 ˚C, and mean total walleye length increased by 217 mm to 346 mm. It is important to note that projected MAT greater than ~10 ˚C is beyond the scope of our observed values thus are largely speculation.
These lakes clearly show how the effect of climate change is predicted to vary based on current MAT. Lakes with high current MAT are predicted to become too warm to support optimal walleye growing temperatures, thus mean walleye length will decrease. Conversely, lakes with low current MAT are currently well below optimal temperatures for walleye are predicted to warm, thus increasing mean walleye length. Temperature and latitude are correlated (Hansen et al. 2017), thus we predict that the same effect would be observed across latitude. In other words, higher latitude lakes would become warmer, thus supporting larger walleye, while lower latitude lakes would become too warm, and result in smaller walleye.
These lakes clearly show how the effect of climate change is predicted to vary based on current MAT. Lakes with high current MAT are predicted to become too warm to support optimal walleye growing temperatures, thus mean walleye length will decrease. Conversely, lakes with low current MAT are currently well below optimal temperatures for walleye are predicted to warm, thus increasing mean walleye length. Temperature and latitude are correlated (Hansen et al. 2017), thus we predict that the same effect would be observed across latitude. In other words, higher latitude lakes would become warmer, thus supporting larger walleye, while lower latitude lakes would become too warm, and result in smaller walleye.
Figure 10. Predicted change in walleye (Sander vitreus) length for three lakes across Canada in the year 2085 under a + 8.5 ˚C warming scenario.
Conclusion
To address our first hypothesis, we conducted an ANCOVA. Our ANCOVA revealed a strong interaction between depth and angling pressure, and illustrated that deep lakes with high angling pressure still have a high abundance of walleye. This suggests that deep lakes provide refugia from angling pressure, and that the interaction between lake depth and angling pressure better explains walleye abundance than lake depth or angling pressure on their own.
To address our second hypothesis, we created a nonlinear function. We determined that a parabolic equation best fits the data, and the shape of this relationship suggests that walleye have an ideal temperature range in the middle, with extreme temperatures limiting their length. We also modeled change in walleye length in future climate scenarios and found that depending on MAT, walleye will either increase or decrease in total length. Therefore walleye in lakes with high current MAT will be smaller and walleye in low current MAT will be larger.
Results from this study will provide insight into how walleye fitness and abundance are affected by climate change and angling pressure. Understanding how these effects impact walleye will help guide management of walleye populations in the future.
To address our second hypothesis, we created a nonlinear function. We determined that a parabolic equation best fits the data, and the shape of this relationship suggests that walleye have an ideal temperature range in the middle, with extreme temperatures limiting their length. We also modeled change in walleye length in future climate scenarios and found that depending on MAT, walleye will either increase or decrease in total length. Therefore walleye in lakes with high current MAT will be smaller and walleye in low current MAT will be larger.
Results from this study will provide insight into how walleye fitness and abundance are affected by climate change and angling pressure. Understanding how these effects impact walleye will help guide management of walleye populations in the future.